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(A) with students' objections to particular activities, so long as the groups they give money to will be
Whoa, there’s all sorts of weird crap in (A). For starters, “universities may collect student activity fees even
with students’ objections to particular activities” literally seems to be saying that activity fees and objections are collected together, somehow. And that doesn’t make sense.
I’m also not thrilled with the pronouns. I’m OK with the “their” at the very end of the sentence, because that seems to refer to the most recent plural noun (“groups”), but I don't love the phrase “they give money to.” I guess “they” is trying to refer to “public universities”, but we have a whole bunch of other plural nouns in the way (“student activity fees”, “students’ objections”, “activities”).
Of course, pronoun ambiguity isn’t an absolute rule on the GMAT (as discussed in
this video), but it’s really not awesome when the pronouns are somewhat confusing. Maybe the pronoun isn’t WRONG, but it’s not ideal, either.
I also have absolutely no idea why the future tense “will be” appears in this sentence.
So we have plenty of good reasons to ditch (A).
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(B) if they have objections to particular activities and the groups that are given the money are
The first “they” is definitely wrong in (B). The only plural nouns earlier in the sentence are “public universities” and “activity fees”, and neither of those make sense. The sentence is trying to say that universities can collect fees even if
students have objections to particular activities – and the only form of “students” in the sentence is actually an adjective (“student activity fees”).
There’s also a meaning issue that stems from the parallelism in (B). We have: “…public universities may collect student activity fees
even if they have objections to particular activities and
the groups that are given the money are chosen without regard to their views.”
That doesn’t actually make sense: the sentence is not trying to say that universities may collect fees
even if groups receive money without regard to their views. The sentence is trying to say that universities may collect fees
as long as the groups receive money without regard to their views. That last part is a requirement imposed by the Supreme Court, so it’s wrong to precede the phrase with “even if.”
So (B) is out.